Calculating Polar Areas

Topic Page

Questions

• How do you find the area of the region bounded by the polar curve #r=3cos(theta)# ?
• How do you find the area of the region bounded by the polar curve #r=3(1+cos(theta))# ?
• How do you find the area of the region bounded by the polar curve #r=2-sin(theta)# ?
• How do you find the area of the region bounded by the polar curve #r^2=4cos(2theta)# ?
• How do you find the area of the region bounded by the polar curve #r=2+cos(2theta)# ?
• How do you find the area of the region bounded by the polar curves #r=sqrt(3)cos(theta)# and #r=sin(theta)# ?
• How do you find the area of the region bounded by the polar curves #r=1+cos(theta)# and #r=1-cos(theta)# ?
• How do you find the area of the region bounded by the polar curves #r=cos(2theta)# and #r=sin(2theta)# ?
• How do you find the area of the region bounded by the polar curves #r^2=cos(2theta)# and #r^2=sin(2theta)# ?
• How do you find the area of the region bounded by the polar curves #r=3+2cos(theta)# and #r=3+2sin(theta)# ?
• If a sprinkler distributes water in a circular pattern, supplying water to a depth of #e^-r# feet per hour at a distance of r feet from the sprinkler, what is the total amount of water supplied per hour inside of a circle of radius 11?
• How do you use the polar coordinates to find the volume of a sphere of radius 10?
• How do you evaluate the integral #sin(x^2+y^2)dr# where r is the region #9<= x^2 + y^2 <= 64# in polar form?
• How do you find the area between #r=1+cos(theta#) and #r=1-cos(theta)#?
• How do you use polar coordinates to evaluate the integral which gives the area that lies in the first quadrant between the circles #x^2+y^2=36# and #x^2-6x+y^2=0#?
• What is the area enclosed by #r=theta # for #theta in [0,pi]#?
• What is the area enclosed by #r=theta^2-2sintheta # for #theta in [pi/4,pi]#?
• What is the area enclosed by #r=thetacostheta-2sin(theta/2-pi) # for #theta in [pi/4,pi]#?
• What is the area enclosed by #r=theta^2cos(theta+pi/4)-sin(2theta-pi/12) # for #theta in [pi/12,pi]#?
• What is the area enclosed by #r=cos(theta-(7pi)/4)+sin(-theta-(9pi)/12) # between #theta in [pi/12,(3pi)/2]#?
• What is the area enclosed by #r=cos(4theta-(7pi)/4)+sin(theta+(pi)/8) # between #theta in [pi/3,(5pi)/3]#?
• What is the area enclosed by #r=-cos(theta-(7pi)/4) # between #theta in [4pi/3,(5pi)/3]#?
• What is the area enclosed by #r=-thetasin(-16theta^2+(7pi)/12) # between #theta in [0,(pi)/4]#?
• What is the area enclosed by #r=2sin(4theta+(11pi)/12) # between #theta in [pi/8,(pi)/4]#?
• What is the area enclosed by #r=sin(5theta-(13pi)/12) # between #theta in [pi/8,(pi)/4]#?
• What is the area enclosed by #r=2sin(theta+(7pi)/4) # between #theta in [pi/8,(pi)/4]#?
• What is the area enclosed by #r=-sin(3theta-(7pi)/4) # between #theta in [pi/8,(pi)/4]#?
• What is the area enclosed by #r=8sin(3theta-(2pi)/4) +4theta# between #theta in [pi/8,(pi)/4]#?
• What is the area enclosed by #r=-3sin(2theta-(2pi)/4) -theta# between #theta in [pi/8,(3pi)/4]#?
• What is the area enclosed by #r=5sin(-6theta-(5pi)/8) -2theta# between #theta in [pi/8,(3pi)/4]#?
• What is the area enclosed by #r=-sin(theta+(11pi)/8) -theta/4# between #theta in [0,(pi)/2]#?
• What is the area enclosed by #r=-sin(theta+(15pi)/8) -theta# between #theta in [0,(pi)/2]#?
• What is the area enclosed by #r=costheta-sintheta/2 -3theta# between #theta in [0,(pi)/2]#?
• What is the area enclosed by #r=2cos((2theta)/3+(5pi)/3)+4sin(theta/2+pi/4) -theta# between #theta in [0,pi]#?
• What is the area enclosed by #r=7cos((theta)/12-(3pi)/2)+2sin((2theta)/3+(2pi)/3) +theta/3# between #theta in [0,pi]#?
• What is the area enclosed by #r=-2cos((11theta)/12+(3pi)/4)+sin((5theta)/4+(5pi)/4) +theta/3# between #theta in [0,pi]#?
• What is the area enclosed by #r=cos((2theta)/3-(pi)/8)+sin((7theta)/8+(pi)/4) # between #theta in [0,pi]#?
• What is the area enclosed by #r=2cos((5theta)/3-(13pi)/8)-3sin((5theta)/8+(pi)/4) # between #theta in [0,pi]#?
• What is the area enclosed by #r=-9cos((5theta)/3-(pi)/8)+3sin((theta)/2+(3pi)/4) # between #theta in [0,pi/2]#?
• What is the area enclosed by #r=5cos^3((5theta)/6-(pi)/2)+theta^2/2 # between #theta in [0,pi/2]#?
• What is the area enclosed by #r=sintheta/theta-theta^3-theta # between #theta in [pi/12,pi/3]#?
• What is the area under the polar curve #f(theta) = theta # over #[0,2pi]#?
• What is the area under the polar curve #f(theta) = thetasin((3theta)/4 )-cos^3((5theta)/12-pi/2) # over #[0,2pi]#?
• What is the area under the polar curve #f(theta) = theta^2sin((5theta)/2 )-cos((2theta)/3+pi/2) # over #[pi/6,(3pi)/2]#?
• What is the area under the polar curve #f(theta) = theta-thetasin((7theta)/8 )-cos((5theta)/3+pi/3) # over #[pi/6,(3pi)/2]#?
• What is the area under the polar curve #f(theta) = thetasin(-theta )+2cot((7theta)/8) # over #[pi/4,(5pi)/6]#?
• What is the area under the polar curve #f(theta) = theta^2-thetasin(2theta-pi/4 ) +cos(3theta-(5pi)/4)# over #[pi/8,pi/2]#?
• What is the area under the polar curve #f(theta) = theta^2-thetasin(7theta-pi/6 ) +cos(2theta-(5pi)/4)# over #[pi/8,pi/2]#?
• What is the area under the polar curve #f(theta) = theta^2-thetasin(6theta-pi/12 ) +cos(12theta-(5pi)/3)# over #[pi/8,pi/6]#?
• What is the area under the polar curve #f(theta) = 3theta^2+thetasin(4theta-(5pi)/12 ) +cos(2theta-(pi)/3)# over #[pi/8,pi/6]#?
• Show that # int_0^h int_0^x sqrt(x^2+y^2) dy dx = h^3/6 (sqrt(2) + ln( sqrt(2) + 1) ) #?
• How do you find the area of one petal of #r=2cos3theta#?
• How do you find the area of one petal of #r=6sin2theta#?
• How do you find the area of one petal of #r=cos2theta#?
• How do you find the area of one petal of #r=cos5theta#?
• How do you find the area inner loop of #r=4-6sintheta#?
• How do you find the area between the loop of #r=1+2costheta#?
• How do you find the area between the loops of #r=2(1+2sintheta)#?
• How do you find the points of intersection of #r=3(1+sintheta), r=3(1-sintheta)#?
• How do you find the points of intersection of #r=1+costheta, r=1-sintheta#?
• How do you find the points of intersection of #r=2-3costheta, r=costheta#?
• How do you find the points of intersection of #r=4-5sintheta, r=3sintheta#?
• How do you find the points of intersection of #r=1+costheta, r=3costheta#?
• How do you find the points of intersection of #r=theta/2, r=2#?
• How do you find the points of intersection of #theta=pi/4, r=2#?
• How do you find the points of intersection of #r=3+sintheta, r=2csctheta#?
• How do you find the area of the common interior of #r=3-2sintheta, r=-3+2sintheta#?
• How do you find the area of the common interior of #r=4sintheta, r=2#?
• How do you find the area the region of the common interior of #r=a(1+costheta), r=asintheta#?
• Question #4e7fa
• Given the parametric equations #x=acos theta# and #y=b sin theta#. What is the bounded area?
• Find the area bounded by the inside of the polar curve # r=1+cos 2theta # and outside the polar curve # r=1 #?
• Find the area of a loop of the curve #r=a sin3theta#?
• Question #f1f96
• What is the area inside the polar curve #r=1#, but outside the polar curve #r=2costheta#?
• What is the area bounded by the the inside of polar curve #1+cos theta# and outside the polar curve #r(1+cos theta)=1#?
• Calculating areas bounded by polar curves looks extremely difficult. Do Americans really need to integrate such a complex expressions without a calculator?
• Find the area bounded by the polar curves? #r=4+4cos theta# and #r=6#
• Using integrals, find the area of the circle #x^2 + y^2 = 1# ?
• Find the area of a single loop in curve #r=\sin(6\theta)#?
• Find the area of the region inside these curves?